• 통합자연과학논문집
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• 제9권1호
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• 대한전기학회논문지
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• 제32권2호
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• pp.43-49
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• 1983

In this study, model simplification problem using singular perturbation technique is considered. The correctness and errors of simplified model which is obtained by the use of this technique, depends upon the order and the time scaling factor of the simplified model But, unfortunately, there is no explicit criteria for selections of these parameters. In this paper, error equations are derived and expanded by using the useful properties of $L_2$-norm. Then, new criteria for selecting the order of the simplified model and time scaling factor with respect to error bound are suggested. Since these criteria, newly proposed in this study, have strong concern about error bound, it can be used to choose the minimum order of the simplified model and time scaling factor with respect to given error bound. Conversely, if the order of the simplified model and time scaling factor are given, the error induced by the simplification can also be computed easily.

• 대한수학회논문집
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• 제35권4호
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• pp.1193-1202
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• 2020

We consider the integral ${{\int}_{0}^{\infty}}(\frac{sin\;x}{x})^n\;dx$ as a function of the positive integer n. We show that there exists an asymptotic series in ${\frac{1}{n}}$ and compute the first terms of this series together with an explicit error bound.

• 대한수학회지
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• 제45권6호
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.22-32
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• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• International Journal of Control, Automation, and Systems
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• 제4권6호
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• pp.697-704
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• 2006

The paper is concerned with $H_{\infty}$ filtering for descriptor systems. A necessary and sufficient condition is established in terms of linear matrix inequalities(LMIs) for the existence of normal filters such that the error systems are admissible and the transfer function from the disturbance to the filtering error output satisfies a prescribed $H_{\infty}$-norm bound constraint. When these LMIs are feasible, an explicit parameterization expression of all desired normal filter is given. All these results are yielded without decomposing the original descriptor systems, which makes the filter design procedure simple and direct. Finally, a numerical example is derived to demonstrate the applicability of the proposed approach.

• ETRI Journal
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• 제15권3_4호
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• pp.1-26
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• 1994

Simulated annealing is an attractive, but expensive, heuristic method for approximating the solution to combinatorial optimization problems. Attempts to parallel simulated annealing, particularly on distributed memory multicomputers, are hampered by the algorithm's requirement of a globally consistent system state. In a multicomputer, maintaining the global state S involves explicit message traffic and is a critical performance bottleneck. To mitigate this bottleneck, it becomes necessary to amortize the overhead of these state updates over as many parallel state changes as possible. By using this technique, errors in the actual cost C(S) of a particular state S will be introduced into the annealing process. This paper places analytically derived bounds on this error in order to assure convergence to the correct optimal result. The resulting parallel simulated annealing algorithm dynamically changes the frequency of global updates as a function of the annealing control parameter, i.e. temperature. Implementation results on an Intel iPSC/2 are reported.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1997년도 춘계학술발표회논문집(1)
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• pp.15-20
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• 1997

We present the results HELIOS verification against VENUS PWR critical experiments loaded with high plutonium content mixed oxides fuels. The effective multiplication factors are calculated to be slightly supercritical within an acceptable error bound. In the prediction of power shape, HELIOS results are in close agreement with the measured values. The RMS errors of re-normalized calculated fission rate distribution are less than 1.4 % with either explicit or implicit models or micro tubes/rods in each fuel assembly for both ALL-MOX and GD-MOX mock-up cores.

• 한국경영과학회지
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• 제31권1호
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• pp.55-71
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• 2006

We perform a computational study on 0-1 knapsack problems generated under explicit correlation induction. A total of 2000 100-variable test problems are solved. We use two solution methods: (1) a well known heuristic and (2) a representative branch and bound type algorithm. Two different performance measures are considered: (1) the number of nodes needed to find an optimal solution and (2) the relative error of the heuristic solution. We also examine the effect of different joint probability mass functions (pmfs) for the coefficient values on the performance of the solution procedure.